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Friday, April 01, 2005

Are Big Price Moves Predictable? (I)

A large body of evidence in academic studies and more practical undertakings indicates that market prices do not undergo a "random walk" as once thought. The classical "random walk" assumptions of normality (i.e., price changes fit a Gaussian distribution) and independence (i.e., the market has no memory) do not agree with "real world" observations of market price movement. Books such as Benoit Mandelbrot's The Misbehavior of Markets (I have read about this book but have not read the book itself) review this topic, explaining how distributions have non-Gaussian "fat tails" and how volatility tends to cluster.

(Footnote: During my graduate student days in the 1980s, I served on our department's seminar committee and had the privilege of inviting Mandelbrot to deliver a lecture. I found him to be a pleasant man to converse with. During his visit, he showed us many fractal charts that, to the human eye, were indistinguishable from market price charts. I recall asking him about predictability of future price movement but do not recall getting a useful answer.)

From a practitioner's point of view, what the academic discussion boils down to is two statements: a) large price swings occur more frequently than we might think, and b) a volatile market tends to remain volatile for some time. Academics have applied chaos theory to describe this price behavior, pointing out how markets tend to be bi-modal, with "chaotic" periods (like an earthquake with its aftershocks) interspersed between "quiet" periods with comparatively little price movement.

The shortcoming of all of this research is that it is descriptive rather than predictive. It describes the nature of the market but does not offer any insight into how one might go about trying to use what we know today to predict where prices will go in the future. In other words, the theory is interesting, but it does not tell us how to make a profit based on the new insight.

So, we are left on our own to attempt the (presumably formidable) task of trying to find pockets of predictability in the market. (I imagine that this problem is no simpler than trying to predict earthquakes.) Because random price behavior is a priori unpredictable, my guess is that any predictability of market price behavior is likely to show up in the non-random, "fat tail" part of the distribution where price behavior is most erratic. Consequently, I think it may be fruitful to focus on large price swings.

Everyday in the market, there are a number of stocks that rise 10% or 20% or more, and others that fall a similar percentage. If we could predict when any of these big price moves are about to occur, we could, of course, become zillionaires by going long or short if we know the direction of the upcoming price swing (or buying puts and calls if we know that higher volatility is imminent but do not know the direction of the upcoming price movement). Alternatively, rather than searching quiet periods for signs of impending volatility, it may easier to turn the problem "on its head" and look for predictable behavior in the wake of large price swings.

The general problem is: Does the price time series itself have any information that tells us when big price movements will occur and what their direction will be? In particular, at the extremes of large price movement, which of the following is more correct?

1. Momentum: A large price advance (decline) indicates that prices will advance (decline) further, or2. Reversion: A large price advance (decline) indicates prices will decline (advance), reverting to the mean after having overshot.

If either of the above is significantly more likely than the other, we will have directional information on price movement that we can exploit to generate excess trading profits.

In subsequent posts, I will report on my progress as I proceed with this study.

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